4MA0 Foundation January 2018 Paper 2R Q19
19
(a) Solve the inequality \(4 - 8p > 11\) (2)
(b) Expand and simplify \((x + 3)(x - 6)\) (2)
(c) Simplify \(\dfrac{y^{12}}{y^4}\) (1)
(d) Simplify \((3e)^2\) (2)
\(\dfrac{2^{11}}{2^2 \times 2^3} = 4^n\)
(e) Find the value of \(n\). (2)
| Scheme | Marks |
|---|---|
| \(4 > 11 + 8p\) or \(-8p > 11 - 4\) or \(-8p > 7\) or \(8p \lt 4 - 11\) or \(8p \lt -7\) | M1 |
| \(p \lt \dfrac{-7}{8}\) | A1 |
| (2) |
Notes
M1: Accept \(4 = 11 + 8p\) or
\(-8p = 11 - 4\) or \(\dfrac{-7}{8}\) or \(8p = 4 - 11\)
A1: Condone \(p \lt -0.875\)
Mark the final answer
| Scheme | Marks |
|---|---|
| \(x^2 + 3x - 6x - 18\) | M1 |
| \(x^2 - 3x - 18\) | A1 |
| (2) |
Notes
M1: For 3 correct terms or
For 4 correct terms ignoring signs or
For \(x^2 - 3x + c\) for any non-zero value of \(c\) or
For ... \(- 3x - 18\)
| Scheme | Marks |
|---|---|
| \(y^8\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(9e^2\) | B2 |
| (2) |
Notes
B2: B1 for 9 or \(e^2\) as part of a product or for \(3^2 \times e^2\)
| Scheme | Marks |
|---|---|
| M1 | |
| 3 | A1 |
| (2) |
Notes
M1: For \(2^{11-2-3}\) or \(2^6\) or 64 or \(4^3\) or \(2^{2n}\)
A1: Accept \(4^3\)